Settle3D Liquefaction Theory Manual

Settle3D Liquefaction Theory Manual

Liquefaction Analysis Theory Manual

2014 Rocscience Inc.

1

Table of Contents 1 Introduction ....................................................................................................................................... 2

2 Theory ................................................................................................................................................ 2

3 Standard Penetration Test (SPT) Based Calculations ................................................................... 3

3.1 Cyclic Stress Ratio (CSR) ........................................................................................................ 3

3.2 Stress Reduction Factor, rd ..................................................................................................... 4

3.3 SPT-N Value Correction Factors ............................................................................................ 7

3.3.1 Overburden Correction Factor, CN ..................................................................................... 7

3.3.2 Hammer Energy Efficiency Correction Factor, CE ............................................................ 9

3.3.3 Borehole Diameter Correction Factor, CB .............................................................................. 9

3.3.4 Rod Length Correction Factor, CR .................................................................................... 10

3.3.5 Sampler Correction Factor, CS .......................................................................................... 11

3.4 Cyclic Resistance Ratio (CRR) .............................................................................................. 11

3.5 Relative Density, DR .............................................................................................................. 16

3.6 Fines Content Correction ...................................................................................................... 17

3.7 Magnitude Scaling Factor, MSF ........................................................................................... 18

3.8 Overburden Correction Factor, K ........................................................................................ 19

3.9 Shear Stress Correction Factor, K ...................................................................................... 22

4 Cone Penetration Test (CPT) Based Calculations ........................................................................ 23

5 Velocity (Vs) Measurement Based Calculations............................................................................ 30

6 Post-Liquefaction Lateral Displacement ....................................................................................... 32

7 Post-Liquefaction Settlement......................................................................................................... 38

References ............................................................................................................................................... 42

Table of Symbols .................................................................................................................................... 45

2

1 Introduction

Liquefaction of soils is a major cause of both damage and loss of life in earthquakes (e.g.; the 1964

Alaska and Niigata, 1983 Nihonakai-Chubu, 1987 Elmore Ranch and Superstition Hills, 1989 Loma

Prieta, 1993 Kushiro-Oki, 1994 Northridge, 1995 Hyogoken-Nambu (Kobe), 1999 Izmit earthquakes).

Researchers have tried to quantify seismic soil liquefaction initiation risk through the use of both

deterministic and probabilistic techniques based on laboratory test results and/or correlations of

insitu index tests with field case history performance data.

Settle3D offers different methods of calculating the factor of safety associated with liquefaction

resistance, probability of liquefaction, and the input parameters required for those calculations. This

manual also describes a simplified method for calculating the lateral spreading displacement as well

as the vertical settlement due to liquefaction.

2 Theory

The use of in situ index testing is the dominant approach for assessment of the likelihood of triggering or initiation of liquefaction. There in-situ test methods have now reached a level of sufficient maturity as to represent viable tools for this purpose. The following tests are often used:

Standard Penetration Test (SPT)

Cone Penetration Test (CPT)

Shear Wave Velocity (VST)

The potential for liquefaction can be evaluated by comparing the earthquake loading (CSR) with the

liquefaction resistance (CRR) - this is usually expressed as a factor of safety against

Liquefaction:

=7.5

where

7.5 = cyclic resistance ratio for an earthquake with magnitude 7.5 = magnitude scaling factor = overburden stress correction factor = ground slope correction factor

3

3 Standard Penetration Test (SPT) Based Calculations

This section summarizes the methods available for calculating liquefaction resistance based on SPT

data. The following are presented:

Cyclic Stress Ratio (CSR)

Stress Reduction Factor (rd)

SPT N-Value Correction Factors

Cyclic Resistance Ratio (CRR)

Relative Density (DR)

Fines Content Correction

Magnitude Scaling Factor (MSF)

Overburden Correction Factor

Shear Stress Reduction Factor

3.1 Cyclic Stress Ratio (CSR)

The cyclic stress ratio, CSR, as proposed by Seed and Idriss (1971), is defined as the average cyclic

shear stress, , developed on the horizontal surface of soil layers due to vertically propagating shear waves normalized by the initial vertical effective stress,

, to incorporate the increase in shear

strength due to increase in effective stress. By appropriately weighting the individual stress cycles

based on laboratory test data, it has been found that a reasonable amplitude to use for the average or equivalent uniform stress, , is about 65% of the maximum shear stress.

=

= 0.65 (

) (

)

where

= maximum horizontal ground surface acceleration (g)

= gravitational acceleration

= total overburden pressure at depth z

= effective overburden pressure at depth z

= stress reduction factor

4

3.2 Stress Reduction Factor, rd

The stress reduction factor, rd, is used to determine the maximum shear stress at different depths in

the soil. Values generally range from 1 at the ground surface to lower values at larger depths.

The following formulations are provided in Settle3D:

NCEER (1997)

Idriss (1999)

Kayen (1992)

Cetin et al. (2004)

Liao and Whitman (1986a)

NCEER (1997)

= 1.0 0.00765 9.15

= 1.174 0.0267 9.15 < 23

= 0.744 0.008 23 < 30

= 0.50 > 30

where

= depth in meters

Idriss (1999)

ln() = () + ()

() = 1.012 1.126 sin (

11.73+ 5.133)

() = 0.106 + 0.118 sin (

11.28+ 5.142)

where

= depth in meters 34

5

= earthquake magnitude

Kayen (1992)

= 1 0.012

where

= depth in meters

Cetin et al. (2004)

(, , , ,12 ) =

[1 +23.013 2.949 + 0.999 + 0.0525,12

16.258 + 0.2010.341(+0.0785,12 +7.586)

]

[1 +23.013 2.949 + 0.999 + 0.0525,12

16.258 + 0.2010.341(0.0785,12 +7.586)

]

for z

6

Notes:

- If the site stiffness estimation is difficult, take ,12 150-200m/s.

- For very soft sites with ,12 less than 120m/s, use a limiting stiffness of 120m/s in

calculations.

- For very stiff sites, ,12 with stiffness greater than 250m/s, use 250m/s as the limiting value

in calculations.

Liao and Whitman (1986a)

= 1.0 0.00765 for z9.15m

= 1.174 0.0267 for 9.15 m

7

3.3 SPT-N Value Correction Factors

Before the CRR can be calculated, the N values obtained from the SPT must be corrected for the

following factors: overburden, rod length, non-standard sampler, borehole diameter, and hammer

energy efficiency, resulting in a(1)60 value. The equation below illustrates the correction.

60 =

(1)60 = 60

The equations used to calculate the correction factors are summarized below.

Table 1.1: Summary of Correction Factors for Field SPT-N Values

Factor Equipment Variable Term Correction

Overburden Pressure CN Section 3.3.1

Energy Ratio

Donut hammer

CE

0.5-1.0

Safety hammer 0.7-1.2

Automatic hammer 0.8-1.3

Borehole Diameter

65 mm -115 mm

CB

1.0

150 mm 1.05

200 mm 1.12

Rod Length

8

Liao and Whitman (1986)

= (1

0 )

0.5

1.7

= (

)

0.5

Bazaraa (1967)

=4

1 + 20 0

1.5

=4

3.25 + 0.50 0

> 1.5

2.0

Idriss and Boulanger (2004)

= (

)

0.7840.0768(1)60

1.7

(1)60 46

Peck, Hansen, and Thorburn (1974)

= 0.77 log (2000

0 ) 0

282

Kayen et al. (1992)

=2.2

1.2 +

1.7

9

3.3.2 Hammer Energy Efficiency Correction Factor, CE

The energy efficiency correction factor is calculated using the measured energy ratio as follows.

=

60

It varies from 0.5-1.3. The ranges are taken from Skempton (1986).

Hammer Type CE

Donut hammer 0.5-1.0

Safety hammer 0.7-1.2

Automatic hammer 0.8-1.3

More specifically,

Hammer Type CE

Automatic Trip 0.9-1.6

Europe Donut Free fall 1.0

China Donut Free Fall 1.0

China Donut Rope& Pulley 0.83

Japan Donut Free Fall 1.3

Japan Donut Rope& Pulley 1.12

United States Safety Rope& pulley 0.89

United States Donut Rope& pulley 0.72

United States Automatic Trip Rope& pulley 1.25

3.3.3 Borehole Diameter Correction Factor, CB

The following table, from Skempton (1986) summarizes the borehole diameter correction factors for

various borehole diameters.

Borehole Diameter (mm) CB

65-115 1.0

150 1.05

200 1.15

10

3.3.4 Rod Length Correction Factor, CR

The rod length correction factor accounts for how energy transferred to the sampling rods is affected

by the rod length.

Youd et al. (2001)

The following table from Youd et al (2001) summarizes the rod correction factor for various rod

lengths. The rod length above the ground must also be added to obtain the total rod length before

choosing the appropriate correction factor.

Rod Length (m) CR

11

3.3.5 Sampler Correction Factor, CS

The sampler correction factor is applied in cases when the split spoon sampler has room for liner

rings, but those rings were not used.

Cetin et al. (2004)

CS Condition Reference

= 1.0 Standard sampler (NCEER, 1997) = 1.0 1.3 Sampler without liners (NCEER, 1997)

= 1.1 1,60 10 (Cetin et al, 2004)

= 1 +1,60100

10 1,60 30 (Cetin et al, 2004)

= 1.3 1,60 30 (Cetin et al, 2004)

3.4 Cyclic Resistance Ratio (CRR)

The cyclic resistance ratio is the other term required to calculate the factor of safety against

liquefaction. The cyclic resistance ratio represents the maximum CSR at which a given soil can

resist liquefaction. The equation for CRR, corrected for overburden pressure and magnitude, is:

= 7.5

The following methods of calculating CRR are for CRR7.5 and still need to have the MSF correction

factors applied:

Seed et al. (1984)

Youd and Idriss (2001)


Cetin et al. (2004) Deterministic and Probabilistic

Japanese Bridge Code (JRA 1990)

Liao et al. (1998) Probabilistic

Youd and Noble (1997) Probabilistic

12

Seed et al. (1984)

Figure 2: Liquefaction boundary curves (Seed et al. 1984)

Youd and Idriss (2001)

Figure 3: SPT clean-sand base curve for magnitude 7.5 earthquakes with data from liquefaction case

histories (modified from Seed et al. 1985)

13

The equation implemented in Settle3D is:

7.5 =1

34 (1)60+

(1)60135

+50

[10(1)60 + 45]2

1

200

where (1)60 is the clean sand value (1)60.


In this method, the N1,60 value is corrected for fines and adjusted to an equivalent clean sand value.

(1)60 = (1)60 + (1)60

(1)60 = exp (1.63 +9.7

+ 0.01 (

15.7

+ 0.01)

2

)

=7.5,=1 = exp ((1)60

14.1+ (

(1)60126

)

2

((1)60

23.6)

3

+ ((1)60

25.4)

4

2.8) for (1)60 < 37.5

=7.5,=1 = 2 (1)60 > 37.5

Cetin et al. (2004) Deterministic and Probabilistic

The following formula calculates CRR for a given probability of liquefaction. In this equation, the

correction for fines content is built into the equations for PL and CRR.

((1)60, , , , ) = exp [

(1)60(1 + 0.004) 29.53 () 3.70 (

) + 0.05 + 16.85 + 2.701()

13.32]

((1)60, , , , ) = (

(1)60(1 + 0.004) 13.32 ln() 29.53 ln() 3.70 ln (

) + 0.05 + 16.85

2.70)

where

= probability of liquefaction in decimals

= CSR (not adjusted for magnitude or duration effects)

= percent fines content expressed as an integer (5 35)

= atmospheric pressure (= 1 , 100 ) (same units as a)

= standard cumulative normal distribution

14

1()= inverse of the standard cumulative normal distribution (ie. mean = 0, and standard deviation = 1)

The deterministic analysis is done for a probability of liquefaction of 50% and a factor of safety of 1.

Japanese Bridge Code (JRA 1990)

This method is based on the equivalent clean sand value of N and the particle size distribution of

sand. The method of fines correction implemented is not necessarily the same as the one used in

Idriss and Boulanger (2004). The various methods of calculating fines correction factors will be

discussed in the next section.

=7.5,=1 = 0.0882(1)60 + 0.7

+ 0.255 log (0.35

50) + 3 0.05 50 < 0.6

=7.5,=1 = 0.0882(1)60 + 0.7

0.05 0.6 50 < 2

3 = 0 < 40%

3 = 0.004 0.16 40%

/2

Liao et al. (1998) Probabilistic

15

Youd and Noble (1997) Probabilistic

() = ln (

1 ) = 7.0351 + 2.1738 0.2678(1)60 + 3.0265 ln()

16

3.5 Relative Density, DR

The relative density of a soil is used in the calculation of the overburden correction factor, CN. The

following methods are provided in Settle3D:

Skempton (1986)

1,60 = 41 2

Ishihara (1979)

= 0.06761,60

Tatsuoka et al. (1980)

= 0.06761,60 + 0.0035


= 1,60

46

Ishihara, Yasuda, and Yokota (1981)

= 0.06761,60 + 0.085 10 (0.5

50)

17

3.6 Fines Content Correction

The fines content has been shown to influence 1,60 and a number of equations have been proposed

to account for this.


(1)60 = (1)60 + (1)60

(1)60 = exp (1.63 +9.7

+ 0.01 (

15.7

+ 0.01)

2

)

Youd et al. (2001)

The following method can also be used with an N value corrected for fines content.

(1)60 = + (1)60

= 0 5%

= exp [1.76 (190

)

2

] 5% < < 35%

= 5.0 35%

= 1.0 5%

= [0.99 + (1.5

1000)] 5% < < 35%

= 1.2 35%

Cetin et al. (2004)

(1)60 = (1)60

= (1 + 0.004) + 0.05 (

1,60) 5% 35%

18

3.7 Magnitude Scaling Factor, MSF

As mentioned previously, the CRR equations above need to be corrected for earthquake magnitude (if

the earthquake magnitude is not 7.5).

Tokimatsu and Seed (1987)

= 2.5 0.2

Idriss (1999)

= 6.9 exp (

4) 0.058 1.8

This method can also be found in Idriss and Boulanger (2004).

Andrus and Stokoe (1997)

= (7.5

)2.56


= 6.9 exp (

4) 0.058 1.8

Youd and Noble (1997)

The summary of the 1996/1998 NCEER Workshop proceedings by Youd and Idriss (2001) outlines

various methods for calculating the MSF and provide recommendations for engineering practice.

The following MSF values are for calculated probabilities of liquefaction, the equation for which is

also shown.

() = ln (

1 ) = 7.0351 + 2.1738 0.2678(1)60 + 3.0265 ln()

< 20% =103.81

4.53 < 7

< 32% =103.74

4.33 < 7

< 50% =104.21

4.81 < 7.75

19

Cetin et al. (2012)

= (

=7.5)

= (7.5

)

Figure 6: Variation of c for different ru and

3.8 Overburden Correction Factor, K

In addition to magnitude, the CRR must be corrected for overburden. It is necessary to correct for

overburden because the CRR of sand depends on the effective overburden stress; liquefaction

resistance increases with increases confining stress.

Hynes and Olsen (1999) (NCEER)

= (

)

1

=

=

= 0.7 0.8 40% < < 60% = 0.6 0.7 60% < < 80%

20

Figure 7: Recommended curves for estimating K for engineering practice (from NCEER 1996

workshop)

The parameter f is a function of site conditions, and the estimates above are recommended conservative values for clean and silty sands and gravels.


This method is basically the same as Idriss and Boulanger (2004), except that the limit for K is

higher.

= 1 ln (

) 1.1

=1

18.9 17.3 0.3

= (1)60

46

=1

(18.9 2.55(1)60)

21

Cetin et al. (2004)

The following figure illustrates the recommended values.

Figure 8: K values, shown with NCEER recommendations (for n=0.7 and DR

22

3.9 Shear Stress Correction Factor, K

K is the static shear stress correction factor, used to correct CRR values for the effects of static

shear stresses.


= + exp (

)

= 1267 + 6362 634 exp() 632 exp()

= exp[1.11 + 12.32 + 1.31 ln( + 0.0001)]

= 0.138 + 0.126 + 2.523

=1

ln (100

)

0.35

0.6 0

where

= relative density

= mean effective normal stress

= empirical constant which determines the value of p at which dilatancy is suppressed and depends on the grain type (Q10 for quartz and feldspar, 8 for limestone, 7 for anthracite, and 5.5 for chalk)

= atmospheric pressure

23

4 Cone Penetration Test (CPT) Based Calculations

The Magnitude Scaling Factor, MSF, and Stress Reduction Factor, Rd, equations are the same for

CPT as SPT. These equations can be found in sections 3.7 and 3.2, respectively.

The following methods are available in Settle3D for determining triggering of liquefaction.

Robertson and Wride (1997)

Modified Robertson and Wride (1998)

Boulanger and Idriss (2004)

Moss et al. (2006) Deterministic

Moss et al. (2006) Probabilistic

Robertson and Wride (1997)

= 1.0 0.00765 9.15 = 1.174 0.0267 9.15 < 23

= 0.744 0.008 23 < 30 = 0.50 > 30

=

= [(3.47 log())2 + (1.22 + log())2]0.5

= [

2] [(

)

]

= [

] 100%

= 1.0 = 0.5

= 1.0

The recommended procedure for calculating the soil behaviour type index can be iterative. The

following procedure is outlined in the NCEER summary report (Robertson and Wride, 1997).

1) Assume n = 1.0 and calculate Q using the following equation and calculate Ic with the

equation above.

= [

) [(

)1.0

] = [

]

24

2) If Ic > 2.6, the soil is clayey and not susceptible to liquefaction.

3) If Ic < 2.6, recalculate Cq and Q using n = 0.5 and recalculate Ic.

4) If Ic 2.6, the soil is probably silty. Calculate qc1N using the equations below using n = 0.7

in the equation for CQ. Calculate Ic using the qc1N value.

1 = (

2)

= (

)

1.7

= 1.0 1.64

= 0.4034 + 5.581

3 21.632 + 33.75 17.88 > 1.64

1 = 1

7.5 = 0.833 [11000

] + 0.05 1 < 50

7.5 = 93 [11000

]3

+ 0.08 50 1 < 160

Figure 9: Normalized CPT soil behaviour type chart, proposed by Robertson (1990)

OCR = overconsolidation ratio, = friction angle

25

The soil types from the chart above are listed below:

1 sensitive, fine grained

2 peats

3 silty clay to clay

4 clayey silt to silty clay

5 silty sand to sandy silt

6 clean sand to silty sand

7 gravelly sand to dense sand

8 very stiff sand to clayey sand (heavily overconsolidated or cemented)

9 very stiff, fine grained (heavily overconsolidated or cemented)

Modified Robertson and Wride (1998)

= [(3.47 log ())2 + ( + 1.22)2]0.5

= (

2) (

)

= [

] 100

= =

= ( 100)

2 = (= 0.1 )

This iterative procedure is:

1) Use n=1.0 to calculate Q.

2) If Ic2.6, the exponent for calculating Q changes to n=0.5, and Ic is calculated using qc1N and F.

3) If Ic

26

< 1.26 (%) = 0

1.26 3.5 (%) = 1.753.25 3.7

> 3.5 (%) = 100

= 0 5% = 0.0267( 5) 5 < < 35%

= 0.8 35%

1 =

1 1

1 = 1 + 1

7.5 = 0.833 [11000

] + 0.05 1 < 50

7.5 = 93 [11000

]3

+ 0.08 50 1 < 160

Boulanger and Idriss (2004)

= exp(() + ())

() = 1.012 1.126 sin (

11.73+ 5.133)

() = 0.106 + 0.118 sin (

11.28+ 5.142)

= =

= 0.65() (

)

= (

)1.3380.249(1)

0.264

1.7

21 1 254

= [(3.47 log())2 + (log() + 1.22)2]0.5

27

= (101 )

=

101

100

=

=

1 = 1 + 1

1 = (5.4 +116

) exp (1.63 +9.7

+ 0.01 (

15.7

+ 0.01)

2

)

=7.5, =1 = exp (1

540+ (

167

)2

(1

80)

3

+ (1

114)

4

3)

= 6.9 exp (4

) 0.058 1.8

= 1 ln (

) 1.0

=1

37.3 8.27(1)0.264 0.3

1 211

= 7.5

=

= 1.859(1.1 )3 0

= 1.859(2.163 0.478(1)0.264)3 0

= 0.032 + 4.7 6.0()2

0.4

= 11.74 + 8.34(1)0.264 1.371(1)

0.528 1 69

= 0 2

28

= min ( , 0.035(2 ) (1

)) < < 2

=

= 1.5 exp(2.5) min(0.08, )

= 1.5 exp(2.551 1.147(1)0.264) min(0.08, )

1 21

1 =

0

1 = 0.00005()3 0.0011()2 + 1.0827() 0.6731

= exp (1

24.5 (

161.7

)2

+ (1

106)

3

4.42)

= exp (1

24.5 (

161.7

)2

+ (1

106)

3

4.42) (1 + exp (1

11.1 9.82))

1 = 0.00005()3 0.0011()2 + 1.0827() 0.6731

1 = 1 + 1

Moss et al. (2006)

= exp {1

1.045 + 1(0.110) + (0.001) + (1 + 0.850) 0.848 ln() 0.002 ln() 20.923 + 1.6321()

7.177}

Probability of liquefaction according to this method is also calculated by the following correlation;

= {1

1.045 + 1(0.110) + (0.001) + (1 + 0.850) 7.177 ln() 0.848 ln() 0.002 ln() 20.923

1.632}

29

where

1 = normalized tip resistance (MPa)

= friction ratio (percent)

= normalized exponent

= equivalent uniform stress ratio

= effective overburden stress (kPa)

() = cumulative normal distribution

1() = inverse cumulative normal distribution function

The deterministic analysis is done for a probability of liquefaction of 50% and a factor of safety of 1.

A revised estimate of the normalization exponent is found using the normalized tip resistance,

shown in the figure below.

Figure 10: Proposed CPT normalization exponent curves from Moss et al. (2006), labeled by

normalization exponent, c, values

30

5 Velocity (Vs) Measurement Based Calculations

The Magnitude Scaling Factor, MSF, and Stress Reduction Factor, Rd, equations are the same for

CPT as SPT. These equations can be found in sections 3.7 and 3.2, respectively.

Two methods are available for calculating triggering of liquefaction from velocity data.

NCEER (1997)

These investigators normalized VS1:

1 = (

0 )

0.25

Pa is a reference stress of 100 kPa

= (1100

)2 + /(1 1) /1

where Vs1c is the limiting upper value of Vs1 for liquefaction occurrence, and

Vs1c=220 m/s for sands and gravel with FC 5%



Figure 11: Proposed cyclic stress ratio curves for different fines content (FC)

(Andrus and Stokoe 2000)

31

Juang et al. (2001) (Probabilistic)

1, = 1

= 1 5%

= 1 + ( 5) 5% < < 35%

= 1 + 30 35%

where

= 0.009 0.0109(1/100) + 0.0038(1/100)2

where Vs1 is overburden stress-corrected shear wave velocity

ln [

1 ] = 14.8967 0.06111, + 2.6418ln (7.5)

Figure 12: Vs-based probability cyclic stress ratio curves logistic regression (Juang et al. 2002)

32

6 Post-Liquefaction Lateral Displacement

The LDI is basically the lateral spreading that occurs due to liquefaction. It is calculated by

integrating the maximum shear strains over depth.

=

0

= 1.859 (1.1 (1)60

46)

3

0

The spreadsheet example in Idriss and Boulanger (2008) also imposes the following limit.

: 1.859 (1.1 (1)60

46)

3

0.5

The limiting shear strain can also be calculated from the relative density, with the same limits as

above.

= 1.859(1.1 )3

= 0.032 + 4.7 6.0()2 0.4

= 0.032 + 0.69(1)60 0.13(1)60 (1)60 7

Using the limiting shear strain, , and the factor of safety, the maximum shear strain can be calculated.

= 0 2 =

= min ( , 0.035(2 ) (1

)) < < 2

The following methods are available for calculating :

Zhang, Robertson and Brachman (2004)

Shamoto et al. (1998)

33

Wu et al. (2003)

Cetin et al. (2009)

Zhang, Robertson and Brachman (2004)

Figure 13: Relationship between maximum cyclic shear strain and factor of safety for different

relative densities, Dr, for clean sands

[based on data from Ishihara and Yoshimine (1992) and Seed (1979)]

34


Figure 14: Relationship between normalized SPT N-value, dynamic shear stress ratio and residual

shear strain potential for clean sands

Figure 15: Relationship between normalized SPT N-value, dynamic shear stress ratio and residual

shear strain potential for FC=10%

35

Figure 16: Relationship between normalized SPT-N value, dynamic shear stress ratio, and residual

shear strain potential for FC=20%

Wu et al. (2003)

Figure 17: Estimation of cyclically induced deviatoric strains (Wu et al. 2003)

36

Cetin et al. (2009)

ln() = ln [0.025(1)60, + (,20,1,1) + 2.613

0.004(1)60, + 0.001] 1.880

lim : 5 (1)60, 40 0.05 ,20,1,1 0.60 0% 100%

where ,20,1,1 are CSR values, corresponding to one-dimensional, 20 uniform loading cycles,

under a confining pressure of 100 kPa = 1 atm.

,20,1,1 = ,20

= (

)

1

, = 1 0.005

= 3105

2 + 0.0048 + 0.7222

= 1

where

= cyclic simple shear tests correction factor

= cyclic triaxial tests correction factor

The recommended maximum double amplitude shear strain boundary curves are also shown in the

figure below.

37

Figure 14: Recommended maximum double amplitude shear strain boundary curves

38

7 Post-Liquefaction Settlement

The liquefaction settlement calculations in Settle3D are completely separate from the settlements

from the stress calculations. They are not superimposed in any way.

Vertical displacements from liquefaction occur due to settlement from reconsolidation as well as

shear deformation from lateral spreading.

The liquefaction settlement calculated in Settle3D is caused by the reconsolidation of the liquefied

soil. Reconsolidation strains are calculated, based on the maximum shear strains that developed

during the cyclic loading.

1 =

0

The following formulations (largely graphical methods) for are provided in Settle3D:

Ishihara and Yoshimine (1992)



Wu et al. (2003)

Cetin et al. (2009)

Ishihara and Yoshimine (1992)

Figure 15: Deviatoric and volumetric strain assessment charts

(adapted from Ishihara and Yoshimine 1992)

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Figure 16: volumetric strain assessment chart (adapted from Tokimatsu and Seed 1984)


Figure 17: Relationship between normalized SPT-N value, dynamic shear stress ratio and residual

volumetric strain potential for clean sands

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Figure 18: Relationship between normalized SPT-N value, dynamic shear stress ratio, and residual

volumetric strain potential for FC=10%

Figure 19: Relationship between normalized SPT N-value, dynamic shear stress ratio, and residual

volumetric strain potential for FC=20%

41

Wu et al. (2003)

Figure 20: Cyclically induced volumetric strains (adapted from Wu and Seed 2004)

Cetin et al. (2009)

() = ln [1.879 ln [780.416 (,20,1,1) (1)60, + +2,442.465

636.613(1)60, + 306.732]] 0.689

: 5 (1)60, 40 0.05 ,20,1,1 0.60

Figure 21: Post-cyclic volumetric strain boundary curves (Cetin et al. 2009)

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References

Andrus, R., Stokoe, K. H. (1997), "Liquefaction Resistance Based on Shear Wave Velocity",

Proceedings of NCEER Workshop on Evaluation of Liquefaction Resistance of Soils.

Boulanger, R. W., (2003a). "Relating K to relative state parameter index." J. Geotechnical and

Geoenvironmental Eng., ASCE 129(8), 77073.

Boulanger, R. W., and Idriss, I. M. (2004). "State normalization of penetration resistances and the

effect of overburden stress on liquefaction resistance." Proc., 11th Intl. Conf. on Soil Dynamics and

Earthquake Engineering, and 3rd Intl. Conf. on Earthquake Geotechnical Engineering, Doolin et al.,

eds, Stallion Press, Vol. 2, pp. 484-491.

Cetin, K. O., and Bilge, H. T. (2012) Performance-based assessment of magnitude (duration) scaling factors. J. Geotech. Geoenviron. Eng.,138(3), 324334.

Cetin, K. O., Bilge, H. T.,Wu, J., Kammerer, A. M., and Seed, R. B. (2009). Probabilistic models for cyclic straining of saturated clean sands. J. Geotech. Geoenviron. Eng., 135(3), 371386.

Cetin, K. O., Bilge, H. T.,Wu, J., Kammerer, A. M., and Seed, R. B. (2009). Probabilistic Model for the Assessment of Cyclically Induced Reconsolidation (Volumetric) Settlements. J. Geotech. Geoenviron. Eng., 135(3), 387398.

Cetin K.O., Seed R.B., Der Kiureghian A., Tokimatsu K., Harder L.F. Jr, Kayen R.E., MossR.E.S.

(2004), SPT-based probabilistic and deterministic assessment of seismic soil liquefaction potential, Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 130(12), 1314-1340.

Hynes, M. E., and Olsen, R. S. (1999), Influence of confining stress on liquefaction resistance. Proc., Int. Workshop on Phys. And Mech. Of Soil Liquefaction, Balkema, Rotterdam, The Netherlands, 145-

152.

Idriss I. M., 1999, "An update to the Seed-Idriss simplified procedure for evaluating liquefaction

potential in Proceedings, TRB Workshop on New Approaches to Liquefaction, Publication No. FHWA-

RD-99-165, Federal Highway Administration, January.

I. M. Idriss and R. W. Boulanger, "Estimating K for use in evaluating cyclic resistance of sloping ground." Proc. 8th US Japan Workshop on Earthquake Resistant Design of Lifeline Facilities and

Countermeasures against Liquefaction, Hamada, ORourke, and Bardet, eds., Report MCEER-03-0003, MCEER, SUNY Buffalo, N.Y., 2003, 449-468.

Idriss IM, Boulanger RW., Semi-empirical procedures for evaluating liquefaction potential during

earthquakes. Proc., 11th International conference on soil dynamics and earthquake engineering, and

3rd International conference on earthquake geotechnical engineering, vol. 1. Stallion Press; 2004. p.

3256.

Idriss, I. M., and Boulanger, R. W. (2008). Soil liquefaction during earthquakes. Monograph MNO-

12, Earthquake Engineering Research Institute, Oakland, CA, 261 pp.

Ishihara, K. (1977), "Simple Method of Analysis for Liquefaction of Sand Deposits During

Earthquakes", Soils and Foundations, Vol. 17, No. 3, September 1977, pp. 1-17.

Ishihara, K., Shimuzu, K., and Yamada, Y. (1981), Pore Water Pressures Measured in Sand Deposits During an Earthquake, Soils and Foundations, Vol. 21, No. 4, pp. 85-100.

43

Ishihara, K., and Yoshimine, M. _1992_. Evaluation of settlements in sand deposits following liquefaction during earthquakes. Soils Found., 32(1), 173188.

JRA (1990) , Specification for Highway Bridges: Part V- Seismic Design. Japan Road Association,

Tokyo.

Juang, C. H., Fang, S. Y., Khor, E. H. (2006) First-Order Reliability Method for Probabilistic Liquefaction Triggering Analysis Using CPT, J. Geotech. Geoenviron. Eng., 132(3), 337-350.

Kayen, R. E, Mitchell, J. K., Seed, R. B. Lodge, A., Nishio, S., and Coutinho, R. (1992), "Evaluation of SPT-, CPT-, and shear wave-based methods for liquefaction potential assessment using Loma

Prieta data", Proc., 4th Japan-U.S. Workshop on Earthquake-Resistant Des. Of Lifeline Fac. And

Counterneasures for Soil Liquefaction, Vol. 1, 177-204.

Liao, S. S. C., Veneziano, D., Whitman, R.V. (1988), "Regression Models for Evaluating

Liquefaction Probability", Journal of Geotechnical Engineering, ASCE, Vol. 114, No. 4, pp. 389-

409.

Liao, S. S. C., Whitman, R. V. (1986), "Overburden Correction Factor for SPT in Sand", Journal of

Geotechnical Engineering, ASCE, Vol. 112, No. 3, March 1986, pp. 373-377.

Meyerhof, G. G., 1957. Discussion on research on determining the density of sands by spoon

penetration testing, in Proceedings, 4th International Conference on Soil Mechanics and Foundation

Engineering, London, Vol. 3, p.110.

Moss, R. S. E, Seed, R. B., KAyen, R. E., Stewart, J. P., Der Kiureghian A., Cetin, K. O. (2006) CPT-Based Probabilistic and Deterministic Assessment of In Situ Seismic Soil Liquefaction Potential, J. Geotech. Geoenviron. Eng., 132(8), 1032-1051.

NCEER, 1997, "Proceedings of the NCEER Workshop on Evaluation of Liquefaction Resistance of

Soils", Edited by Youd, T. L., Idriss, I. M., Technical Report No. NCEER-97-0022, December

31, 1997.

Peck, R B Hanson, W E & Thornburn, T H (1974) Foundation engineering Pub: John Wiley, New

York

Robertson, P. K., Wride (Fear), C. E.,(1998) Evaluating cyclic liquefaction potential using the cone penetration test, Can. Geotech. J. 35: 442459 (1998).

Seed, H. B., Idriss, I. M. (1971), Simplified Procedure for Evaluating Soil Liquefaction Potential, Journal of the Soil Mechanics and Foundations Division, ASCE, Vol. 97, No SM9, Proc. Paper 8371,

September 1971, pp. 1249-1273.

Seed, H. B., Idriss, I. M. (1982), "Ground Motions and Soil Liquefaction During

Earthquakes", Earthquake Engineering Research Institute Monograph Series.

Seed, H. B., Idriss, I. M., Arango, I. (1983), "Evaluation of Liquefaction Potential Using Field

Performance Data", Journal of Geotechnical Engineering, ASCE, Vol. 109, No. 3, pp. 458-482.

Seed, H. B., Tokimatsu, K., Harder, L. F., Chung, R. M. (1984), "The Influence of SPT Procedures

in Soil Liquefaction Resistance Evaluations", Earthquake Engineering Research Center Report No.

UCB/EERC-84/15, University of California at Berkeley, October, 1984.

44

Shamoto, Y., Zhang, J., and Tokimatsu, K. (1998). New charts for predicting large residual post-liquefaction ground deformation. Soil Dyn. Earthquake Eng., 17_78_, 427438.

Skempton, A.W. 1986. Standard penetration test procedures and the effects in sands of overburden

pressure, relative density, particle size, ageing and overconsolidation. Geotechnique 36(3): 425-447.

Tokimatsu, K., and Seed, H. B. _1984_. Simplified procedures of the evaluation of settlements in clean sands. Rep. No. UCB/GT-84/16, Univ. of California, Berkeley, Calif.

Tokimatsu, K., and Seed, H. B., 1987. Evaluation of settlements in sands due to earthquake shaking,

J. Geotechnical Eng., ASCE 113 (GT8), 861-78.

Wu, J., Seed, R. B., and Pestana, J. M. (2003). Liquefaction triggering and post liquefaction Geotechnical

Engineering Research Rep. No. UCB/GE-2003/01, Univ. of California, Berkeley,Calif.

Youd, T. L., Hansen, C. M., and Bartlett, S. F., 2002. Revised Multilinear regression equations for

prediction of lateral spread displacement, J. Geotechnical and Geoenvironmental Eng. 128(12),1007-

017.

Youd, T. L., Idriss, I. M., Andrus, R. D., Arango, I., Castro, G., Christian, J. T., Dobry, E., Finn, W. D.

L., Harder Jr., L. F., Hynes, M. E., Ishihara, K., Koester, J. 169 P., Liao, S. S. C., Marcusson III, W.

F., Martin, G. R., Mtchell, J. K., Moriwaki, Y., Power, M. S., Robertson, P. K., Seed, R. B., and Stokoe

II, K. H. (2001). Liquefaction resistance of soils: Summary report from the 1966 NCEER and 1998 NCEER/NSF workshops on evaluation of liquefaction resistance of soils J. Geotechnical and Geoenvironmental Eng., 124(10), 817-833.

Youd, T. L., Noble, S. K. (1997), "Liquefaction Criteria Based on Statistical and Probabilistic

Analyses", Proceedings of the NCEER Workshop on Evaluation of Liquefaction Resistance of

Soils, December 31, 1997, pp. 201-205.

G. Zhang; P. K. Robertson, M.ASCE; and R. W. I. Brachman (2004).Estimating Liquefaction-Induced Lateral Displacements Using the Standard Penetration Test or Cone Penetration Test, J.

Geotechnical and Geoenvironmental Eng. 130(8), 861-871.

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Table of Symbols

amax maximum ground acceleration Mw earthquake magnitude N60 SPT value corrected for energy, rod length, etc. %FC percentage fines content unit weight D50 particlediameter corresponding to 50% passing

H influence depth of SPT reading Cfines correction factor for fines content N1,60 correction factor for fines content (instead of Cfines)

N1,60cs equivalent clean sand N value, fully corrected

CN overburden normalization factor N1,60 SPT normalized to 100 kPa overburden CSR cyclic stress ratio N1,60Sr post-liquefaction N value

PL probability of liquefaction Sr residual shear strength F factor for calculating maximum shear strain lim limiting shear strain CRRM=7.5,=1 cyclic resistance ratio for magnitude M=7.5 and overburden stress=100kPa CRR cyclic resistance ratio, corrected for magnitude and overburden FS factor of safety max maximum shear strain LDI lateral displacement index v vertical reconsolidation strain S vertical reconsolidation settlement

SPT Standard Penetration Test

CPT Cone Penetration Test

Vs Shear Wave Velocity

Vs,12m Site shear wave velocity over the top 12 m

FC Percent fines content passing sieve #200 (clay and silt)

Mw Earthquake magnitude

z Soil depth

av Average cyclic shear stress

g Gravitational acceleration

v Total overburden pressure at the depth z

v Effective overburden pressure at the depth z

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rd Stress reduction factor

MSF Magnitude scaling factor

K Overburden stress correction factor

K Ground slope correction

Pa atmospheric pressure (=1 atm,100 kPa)

standard cumulative normal distribution

-1 (PL) inverse of the standard cumulative normal distribution

ru excess pore pressure ratio

max maximum double amplitude shear strain

CSRss,20,1D,1atm CSR values, corresponding to one-dimensional, 20 uniform loading cycles,

under a confining pressure of 100 kPa =1 atm

Settle3D Liquefaction Theory Manual

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